AP Statistics
Ch11 Practice
Name:____________________
1. In statistics, what is meant by the P-value?
2. Explain the difference between a one-sided alternative hypothesis and a two-sided alternative hypothesis.
3. What is meant by a significance level?
4. What two circumstances guide in choosing a level of significance?
5. Why is it important to always plot your data?
6. What is a Type I Error?
7. What is a Type II Error ?
8. What is the relationship between the significance level α and the probability of Type I Error?
9. What is meant by the power of a significance test?
10. Fill out the following chart with the following: Incorrect Decision, Correct Decision, Type I Error, Type II
Error, Power, α, 1 – α, β, 1 – β
H0 is true
Ha is true
Reject H0
Fail to reject H0
11. State four ways to increase the power of a significance test:
State the null and alternative hypotheses
12. A manufacturer claims that a new brand of air-conditioning unit uses only 6.5 kilowatts of electricity per
day with a standard deviation of 1.4. A consumer agency believes the true figure is higher and runs a
test on a sample of size 50. The sample mean is 7.0 kilowatts.
13. A local chamber of commerce claims that the mean family income level in a city is $12,250. An
economist believes that this is incorrect. He runs a hypothesis test, using a sample of 135 families, and
finds a mean of $11,500 with a standard deviation of $3,180.
14. For each α and observed significance level (p-value) pair, indicate whether the null hypothesis would be
rejected.
a) α = . 05, p = .10
b) α = .10, p = .05
c) α = .01 , p = .001
d) α = .025 , p = .05
e) α = .10, p = .45
15. The one-sample Z statistic for testing
H0: μ = 0
Ha: μ > 0
has the value Z = 1.98.
a) Is the value Z = 1.98 significant at the 5% level? Why?
b) Is the value Z = 1.98 significant at the 1% level? Why?
16. The one-sample Z statistic for the two-sided test of
H0: μ = 0
Ha: μ ≠ 0
has the value Z = -2.58.
c) Is the value Z = -2.58 significant at the 5% level?
a) Is the value Z = -2.58 significant at the 1% level?
17. City Emergency response times to serious accidents are reported at 6.7 minutes. Local officials are
concerned that the actual response times are larger than the report indicates.
H0: μ = 6.7 minutes
Ha: μ > 6.7 minutes
Describe and give the consequences of a Type I error and a Type II error. Decide whether you would
choose an alpha level of 0.01 or 0.1 and explain why.
18. State the probability of a Type I error and the probability of a Type II error.
Perform a FULL TEST for the following
19. A professional pickologist believes that the average times a day a person picks their nose is 3, with a
standard deviation of 1 nose pick. A researcher tests this claim to see if the true average is greater than
3, using an SRS of 500 people. She finds the sample mean to be 3.1 nose picks. Is this sufficient
evidence at the 5% level to reject the professional pickologist’s claim?
20. A pharmaceutical manufacturer does a chemical analysis to check the potency of toe fungus cream. The
standard release potency for the active ingredient, fungicitis-eliminatus, is 20, with a known population
deviation of 3. A sample of 20 lots gives the following potency data:
22
20
18
14
13
26
28
18
25
21
18
16
15
23
28
26
27
21
20
25
Is there significant evidence at the 5% level that the mean potency is not equal to the standard release
potency?